I've found one rare use of First() or Last(), and this was from personal experience early in my career.  In a badly designed table where data aren't normalized, such as in the pictured example below, where the same customer is spelled differently in multiple rows, the only way to make an aggregate query is to use First() or Last().  In this case, the customer field can't be put under GROUP BY because the data are different.  You want the customer to be displayed, so the field has to be in the query somehow.  In an aggregate query, a field has to be either under GROUP BY or an aggregate field.  So the customer field needs to use an aggregate function.  All the other aggregate functions like Sum(), Count(), etc. can't be used, obviously.  So First() or Last() are the only options.  Since all customers are "the same," it doesn't matter which record First() or Last() uses.  Again, this is a case of bad table design.  But there may be cases where you may legitimately have non-normalized data, and First() and Last() may be useful there too.